Relativity Definition and 998 Threads

In relativity, momentum of a body is given by ##p=mv/\sqrt{1-v^2/c^2}##, but if mass is exactly zero and velocity is exactly ##c##, how is the photon momentum even defined? I don't think this problem can be resolved by simply stating the other formula relating energy to momentum, since it was...

Body 1 travels 48 light years from point A to point B at 82% of light speed. Body 2 leaves point A 33 years after Body 1 and travels the 48 light years to point B at 99.99995% of light speed. What I think I know: Body 1 takes 58 years to reach point B according to an earth observer. Body 1...

General relativity permits some exact solutions that allow for time travel. Some of these exact solutions describe universes that contain closed timlike curves, or world lines that lead back to the same point in spacetime. I wondered if these solutions also permits Causal loops? Such as the one...

I was reading a paper by J.M.C Montanus which was published in <low quality journal reference removed> in which he claims under AEST the new gravitational dynamics and electrodynamics are reformulated in close correspondence with classical physics, and subsequently leads to the correct...

Alice measures the spin, also Bob measures. If we assume that the signals (from Alice to Bob) were sent, they had to be with the speed e.g. 10 c But in another frame of reference Bob first measures, next Alice. Measurement of Alice was cause and was sent back in time, or measurement of Bob was...

hi everyone "The principle of relativity: The laws of physics are the same in all inertial reference frames." Is in classical physics The laws of physics aren't the same in all inertial reference frames!? Give an example in classical physics Thanks

Muons are a popular way to provide evidence for Special Relativity. But, does Muon Tomography provide evidence for SR? Can you calibrate your muon detectors without reference to SR? Is there any need to refer to SR when interpreting the data? I tutored a high school student who argued the...

I recently viewed some online free lecture series on Special theory of Relativity. I think I have an understanding of the basics so far, but would like some books for problems on special relativity. (Preferably solutions or at least answer keys included). It would be a great help if they...

In relativity, no signal travels faster than light, and hence if something happened away from me, I will only know about it after some time. This means I cannot measure instantly the position and time of something as it happens; this would violate special relativity. I however imagine that I...

Hello. I'm new here and very much afraid of breaking rules. I would gladly post this question in the Homework section, because it's homework, but my question doesn't fit the template, it's a theory question. I hoped to find it in Relativity FAQ's, but it's not there. I can tell you I grasped...

Sorry for the extra question. Just have a lot of questions lately and I know some people around here are annoyed with that.

Hi everyone, I want to learn relativity but right now I don't know where to start. I have been doing Newtonian mechanics for quite some time from resnik and Irodov and want to go further. Which book should I now read?

In texts on General Relativity, the proper time ##d\tau^2 = -ds^2## (with an appropriate choice of metric signature) is commonly said that the time measured by a timelike observer traveling along a path is given by the integral of ##d\tau## along this path. Of course it's possible to construct a...

In Newtonian mechanics, G is simply a proportionality constant or the force with which two bodies of unit mass attract each other. However, GR doesn't treat gravity as a force. So how is G defined in GR? Is it a property of spacetime or just some useless mathematical artefact? What does G...

hello I'm korean high school student and sorry for my poor English. I saw ## t_0=t_f\sqrt{1 -\frac{ 2GM}{rc^2}} ## in wikipedia. does ## \sqrt{1 -\frac{ 2GM}{rc^2}} ## of this equation have name like lorentz factor ## \frac{1}{\sqrt{1 -\frac{v^2}{c^2}}} ##of ## t=\frac{t_0}{\sqrt{1...

1) really does not make sense to me. It is not clear to me how light could be reflected in multiple directions if the source is not a tilted mirror or another object with specific properties. I think the thought of the "point" P confuses me. Further, the fact that light travels in the opposite...

According to professional scientific literature and to our best understanding, are there any suggestions that entanglement might imply some sort of faster than light signaling between the entangled particles? I know that according to relativity nothing can travel faster than light, but what...

Hi PFs, I am reading this paper written by carlo Rovelli: https://arxiv.org/abs/1010.1939 there are many things that i fail to understand, but i would like to begin with a simple thing. Rovelli write that: It is locally Lorentz invariant at each vertex, in the sense that the vertex amplitude...

We can derive the constancy of the speed of light from Maxwell equations. My questions are: 1. Why it is then need to postulate it when we can obtain it from Maxwell equations? 2. It is stated in many books that gravity wave also propagates with the same speed, c. How do we conclude that? Is...

In this picture it shows a light clock. Let's use the moving light clock example. Am I essentially calculating the b component of moving clock. Assume the moving frame is the B frame. Assume the stationary frame is the A frame https://simple.wikipedia.org/wiki/Light_clock Or essentially the b...

In https://arxiv.org/pdf/1709.07852.pdf, it is claimed in equation (1) and (2) that when we take non-relativistic limit, the following Lagrangian (the interaction part) $$L=g \partial_{\mu} a \bar{\psi} \gamma^{\mu}\gamma^5\psi$$ will yield the following Hamiltonian $$H=-g\vec{\nabla} a \cdot...

I would like to think this is a legitimate question in the fold of Relativity theory. It originally started with the idea that "If someone were to wormhole themselves 2000 or so light years away and turn their sights back on the Earth, they could possibly get a glimpse of the Crucifixion?" On...

In the space-time of special relativity considered as fiber bundle, could it be stated that the base space is time and the fibers are space ##R^3## related to each other by the Lorentz metric as a connection and in this case would there be parallelism, and in this case: how would this fiber...

Listen to the following arguments: Earth's orbit isn't perfect ellipse because classically there is the gravitational field of moon and possibly of Mars and Venus which affect it According to general relativity isn't perfect ellipse because there is the curvature of space time which doesn't...

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

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Hope this question can be quickly clarified: There was a statement that the General Relativity can be interpreted by speaking of an ether whose state varies from point to point. Is this correct?!

I am looking for generalizations of special relativity for flat spacetime. Of course, most well known generlaization of SR is general relativty. There are many other generalizations of SR for curved spacetime. All what I found is for curved spacetime. Are any more or less successfull attempts to...

New member here; just a physics hobbyist. There is probably a simple answer to this question but I could not find it. We know time flows faster on mountaintops relative to sea level due to gravitational time dilation. Over millions of years, wouldn't there be a cumulative effect making the...

I am having a class of general relativity. It seems that the professor will follow an approach which consist of achieve the action, and variate it to get the equations of motion (indeed, that's how we already got the geodesic equation, the dynamics of a particle in electromagnetism, the equation...

According to @vanhees71 and his notes at https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf under certain conditions one can choose ##\tau## as the parameter to parametrize the Lagrangian in special relativity. For instance if we have, $$A[x^{\mu}]=\int d\lambda...

Why in general relativity do we need the physics of perfect fluids?

Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?

Spacetime is a differential manifold and at each point is attached a Minkowski spacetime. There the laws of physics are the usual ones without gravity. Gravity is the curvature of spacetime. To define the concept of curvature do we need to evaluate at least one neighborhood of point P? Is...

Hello, this is my first thread. Robert Wald, in General Relativity, equation (4.2.8) says : E = – pa va where E is the energy of a particle, pa the energy-momentum 4-vector and va the 4-velocity of the particle. How can I see this is compatible with the common energy-momentum-relation E2 – p2 =...

In GR, a free falling object when viewed by a distant observer appears to be length contracted and slows down as it approaches the event horizon of a black hole. The length contraction piece, however, seems counterintuitive. I would have thought that the leading edge of the object would...

Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...

What mathematical topics do I need to know to start studying general relativity? From which textbooks can I learn them? I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and...

Hi, In general relativity, gravitation is not anymore a Force but a deformation of space time. I would like to know what's becomes the 3 law of Newton for gravity that action equal reaction ? When a apple fall on the earth, does "the force" is exactly the same as the one applied on Earth ...

i) The muon reaches the ground ii) To a ground observer, the decay time is dilated $$\Delta t_d=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\Delta\tau_d>\Delta \tau_d$$ The time for the muon to reach the ground is $$\Delta t_g=\frac{10 km}{0.999c}< \Delta t_d$$ which is why it reaches the ground...

Following are not strictly physics questions. But cool questions to discuss. We need to add dark energy to our cosmological model if we strictly follow GR. This lead to some beliefs that GR is an effective theory. (1)Do you believe that GR is the fundamental theory? If GR is an effective...

Hi everybody. I recently started to learn GR from a very begginer level. I would like to share with you some lines of discussion, to understand your approach to some specific topics which for me are key to better understand the whole story. If a put an accelerometer on the floor it reads 9.8...

Can someone explain me difference between A^{\mu}_{\hspace{0.2cm} \nu} A^{\hspace{0.2cm} \mu}_{\nu} and A^{\mu}_{\nu}?

When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...

We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...

A rocket has length L with a separate head on top. The rocket lands in a cilinder on Earth with height L with speed v. From the point of view of the rocket, the cylinder undergoes a Lorentz contraction. The rocket will therefore collide with the bottom of the cilinder and damage it. From the...

Hello! I'm starting to study curved QFT and am slightly confused about the invariance of the Klein Gordon Lagrangian under a linear diffeomorphism. This is $$L=\sqrt{-g}\left(g^{\mu\nu}\partial_\mu \phi \partial_\nu \phi-\frac{m^2}{2}\phi^2\right),$$ I don't see how ##g^{\mu\nu}\to...

Given what we know about special relativity and its implication for time and the observer, could this in any way be linked to why the isolated processes of QM are exhibiting everything happening at once and then collapsing to classical physics when bigger objects interact - the measurement...

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In both Wald and Carroll, a type (k,l) tensor has k dual vectors and l vectors, yet a (1,0) tensor is a vector and a (0,1) tensor is a dual vector. I must be missing something simple. Please explain.